If vec$(A)=3$hat$(i)-$hat$(j)+4$hat$(k)$ and vec$(B)=$xhat$(i)+$hat$(j)-5$hat$(k),$ find $x$ so vec$(B)$ will be perpendicular to vec$(A).$

Determine the angle between the directions of vector vec$(A)=-3\mathrm{.}00$hat$(i)+1\mathrm{.}00$hat$(j)+1\mathrm{.}00$hat$(k)$ and vector vec$(B)=1\mathrm{.}00$hat$(i)-3\mathrm{.}00$hat$(j)-2\mathrm{.}00$hat$(k).$

Please write it out on paper with all the steps.